OP, here. Back on the subject on which this thread began:
I have started rereading Bruce Barnbaum's The Art of Photography (1st edition). I recommend his early chapters to any who are interested in thinking about composition. While he discusses the various visual elements of composition, he places them appropriately, in my view, in a most thoughtful discussion of approach to photography. Copies are available for very little; later editions a bit (or much) more. Inter-library loan programs are also a valuable resource.